A particle moves with simple harmonic motion in a straight line. In the first s, after starting from rest, it travels a distance a, and in next s it travels 2a, in the same direction, then:
(1) amplitude of motion is 4a
(2) time period of oscillations is 6
(3) amplitude of motion is 3a
(4) time period of oscillations is 8
The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and the ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3 , the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to (ln 5 = 1.601, ln 2 = 0.693) :
(1) 231 s
(2) 208 s
(3) 161 s
(4) 142 s
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = cos, and y = traces a curve given by:
(1)
(2)
(3)
(4)
The angular frequency of the damped oscillator is given by, where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio is 8%, the change in the time period compared to the undamped oscillator is approximately as follows:
(1) increases by 1%
(2) increases by 8%
(3) decreases by 1%
(4) decreases by 8%
Which of the following expression corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?
(1) a + bx - c
(2) b
(3) a - bx + c
(4) -bx
Match List - I (Event) with List-II (order of the time interval for happening of the event) and select the correct option from the options given below the lists:
(A) |
Rotation period of earth |
(i) |
|
(B) |
Revolution period of earth |
(ii) |
|
(C) |
Period of a light wave |
(iii) |
|
(D) |
Period of a sound wave |
(iv) |
(1) (A)-(i),(B)-(ii), (C)-(iii), (D)-(iv)
(2) (A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)
(3) (A)-(i), (B)-(ii), (C)-(iv), (D)-(iii)
(4) (A)-(ii), (B)-(i), (C)-(iii), (D)-(iv)
A body is in simple harmonic motion with a time period of half-second (T = 0.5 s) and amplitude one cm (A = 1 cm). Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.
(1) 4 cm/s
(2) 6 cm/s
(3) 12 cm/s
(4) 16 cm/s
In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the square of the measured time period is plotted against the string length of the pendulum in the (Fig. 9.18). What is the value of g at the place?
(1) 9.81 m/
(2) 9.87 m/
(3) 9.91 m/
(4) 10.0 m/
For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents this correctly? (Graphs are schematic and not drawn to scale)
(1)
(2)
(3)
(4)
A pendulum with a time period of 1s is losing energy due to damping. At a certain time, its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant is:
(1)
(2)
(3) 2
(4)
A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant when it is at a distance 2A/3 from the equilibrium position. The new amplitude of the motion is:
(1) 3A
(2) A
(3)
(4)
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are the same and equal to A and T, respectively. At time t = 0 one particle has displacement A while the other one has displacement -A/2 and they are moving towards each other. If they cross each other at time t, then t is:
(1) T/6
(2) 5T/6
(3) T/3
(4) T/4
A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like :
(1)
(2)
(3)
(4)
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is:
(1)
(2)
(3)
(4) 2 Hz
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 . At, t = 0, the displacement is 5 m. What is the maximum acceleration? The initial phase is .
(1) 500
(2) 500
(3) 750
(4) 750